PD0002

Lt(a,b)

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

Witness-defined strict order on natural numbers.

Conservative notation; not a theorem, primitive, or axiom.

Definition in prerequisite notation

S a ≤ b

Only definitions earlier in this acyclic notation graph are used here.

Hygienic expanded first-order definition 
exists h. h + S a = b

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

none — first-order arithmetic only

Definitions depending on this notation

DivRem(n,d,q,r)Product(b,c,l,z)Repeat(b,c,a,l)BoundedPrefix(b,c,l)InjectivePrefix(b,c,l)UnitBitPrefix(n,b,c,l)Sum(b,c,l,z)SurjectivePrefix(b,c,l)Unit(a,m)CanonicalModularResidue(m,a,r)UnitMultiplierPrefix(a,m,b,c,l)UnitProductPrefix(m,b,c,l)UnitScaledPrefix(a,m,b,c,d,e,l)

Checked theorems using this definition

EU0005 · euler_coprime_modular_unitEU0008 · euler_multiplier_prefix_extendEU000A · euler_multiplier_prefix_entryEU0013 · euler_unit_product_prefix_extendEU0016 · euler_unit_product_prefix_entryEU001B · euler_unit_product_reindex_scaleEU001F · euler_coprime_totient_power_valueEU0022 · euler_theorem_for_units